My questions centers around what method is best to use parametrize a response function for an experiment. We are currently using ab initio simulation to model our experiment's response. Unfortunately, this is very compute intensive and wasteful, e.g. 500x compute time for every second we run the experiment.
Our input would be a set of parameters random chosen from a known and samplable PDF. From this vector we want to skip the ab initio simulation. Rather we would like to put this into an AI model to give us a statistically likely result, either by allowing us to do importance sampling (answer "Will this actually show up in our experiment?") and/or give us a statistically likely output of the ab initio simulation (answer "If it shows up, what does it show up as?").
We have been able to parametrize a subset of the simulation outputs (the second question above) using B-splines. Adding the missing pieces to the splines has proven prohibitive at this stage. We want to try an AI method to do this parametrization.
To throw a wrench into the whole thing is that we care about the (long) tails of the distribution, i.e. the rare things are interesting. VAEs, GANs, and other generative models tend to struggle in the tails of the distribution. We could be using a MCMC/importance sampling method, but I don't think that will be any less computationally expensive than the "ab initio" simulation.
The question boils down to is there a good AI-based generative model, functional approximiator, or dimensionality reduction method for this?